We propose to cover various modalities in radiology -- namely, computerized tomography (CT), positron emission tomography (PET), magnetic resonance imaging (MRI) and ultrasound (US) -- all of which are tomographic in the sense that they produce images of slices through the human body. "Reconstruction" in the title of the proposal is to be interpreted as the procedure to produce such images from the measured raw data in CT, PET, and MRI. "Display" in the title is to be interpreted as the procedure to put together in three-dimensional (3D) or (including time) 4D -- space the information that exists in the individual slices. In "reconstruction" we plan to concentrate on iterative finite series- expansion methods, preprocessing of incomplete or distorted data, applications to PET and MRI, and methods for objective evaluation of reconstruction algorithms. In "display" we plan to concentrate on segmentation (identification of structures of interest, such as specific organs, in the 3D space), the use of color for displaying medical images, computerized 3D radiation therapy treatment planning, and 3D display, quantitation and analysis of the normal, ischemic and infarcted left ventricle, of normal and disturbed flow, and of complex congenital heart disease. In all caSes computer software will be fully developed, implemented, tested, and evaluated, on the kind of computing equipment that is commonly available to radiology departments. Supplemental funding is requested for the last seven months of the currently active grant for the projects which involve applications to cardiology. Further supplemental funding is requested for seventeen months beyond the end of the currently active grant for all the projects listed above.